Best Ways to Improve Mathematic Abilities?

Forgive me if this is the wrong place to be posting this, but as far as I can tell, this is the most appropriate place to post my question that I can find.

My main question is obviously the title of this thread, but I figured that it would be best for me to give you some background information about my own mathematic abilities in order to make it easier for a response:

I'm currently a sophomore in higschool, and am one year ahead in math, take all Honors and AP classes, but in math, I always seem to struggle to get Bs. It's discouraging to see other people in my class, some of them even a year younger than me, who seem to grasp the concepts with ease, while I'm going home and spending hours going through problems just trying to make sure I know everything.

Now, unfortunately, I fear that my intelligence and my ability to do well in school revolves around my memory and my ability to write well. I would easily give up those skills to obtain a more analytical mind so that I could potentially pursue a career in Physics, and not be way in over my head.

So, my main question is this: Are there any definitive ways for somebody to improve at math? I've heard that a lot of it is the ability to get the main ideas of it down, and to then learn how to apply those concepts to more complicated ideas. Would it be best for me to almost re-learn the basics of each course that I've taken so far?

Also, in a related note, is it worth pursuing a career in Physics if it interests me, when I am stronger in other subjects? I try to think of myself as a humble person, but just this year, my English teacher was bombarding me with praise. I got 100% on virtually all of my essays, and in one assignment that I wrote (a prequel to the Scarlet Letter) she told the class (apparently when I was gone that day) that she couldn't have written it better herself. I wrote it in one hour at 2 in the morning..

I'm sort of in a dilemma right now where Physics is my passion, it's what interests me, but my mind appears to work better for other things.

I'm taking AP Physics next year, so as far as I can tell, that will be the best guideline to tell me whether or not I'll be able to just work towards learning and understanding Physics. I'm fully aware that being a phsyicist obviously isn't something for everyone (there's some statistic where the average IQ of a physicist is 148, or something around that), but I want to know if math is something that a person could substantially improve on through hard work, and if so, what the best ways to achieve that goal are.

Just you should remember that practice perfect the man. Also I want to tell you that you should try to improve your mind concentration. Research report told us mind concentration is the main thing. And try to know solution of math different way. One way may be not suitable to you, but another way may be easy to you.

I'm taking AP Physics next year, so as far as I can tell, that will be the best guideline to tell me whether or not I'll be able to just work towards learning and understanding Physics. I'm fully aware that being a phsyicist obviously isn't something for everyone (there's some statistic where the average IQ of a physicist is 148, or something around that), but I want to know if math is something that a person could substantially improve on through hard work, and if so, what the best ways to achieve that goal are.

Thanks for reading.

This may not be the best help you get, but basically I will just tell you what I plan on doing. I'm kind of in the same position as you, except that I'm in the normal math class and I find everything to be exceedingly easy and a waste of time.

So here it goes;

1. This summer I will be testing out of Alg II so next year (sophomore in highschool) I can be in the advanced math class, which is pre-calc at my school.
2. This summer I will also be learning pre-calc/calc from a friend, in hopes that when pre-calc rolls around next year it will be extremely easy.
3. During my sophomore I will start to read through and study Spivak.
4. The summer after my sophomore year I will most likely study linear algebra with my mom.

This is my plan to get alot better at math, just do more than the top student in your school. While the other kids spend their summer doing other miscellaneous things, spend parts of your's doing math. Also, if you have taken physics this year you could possibly look into a higher level of physics. I know that this summer I might do some Algebra based physics, along with programming in C, which I suggest you look into.

I'm currently a sophomore in higschool, and am one year ahead in math, take all Honors and AP classes, but in math, I always seem to struggle to get Bs.

Out of curiosity, do you do any computer programming? Do you have any technical hobbies?

If you post on a physics and math forum and say you are discouraged about your progress in physics and math then naturally the predominant tone of advice is going to be "work harder", "devote yourself". If you want to see the otherside of the coin, you would post on an English literature forum. I haven't looked to see if you've made other posts on the forum. If you've asked questions about homework on the forum then a person could look at them and perhaps say "You've almost got the hang of it" or "Nah, give up, kid." Without some examples, we're just guessing.

You're only a sophomore, so I say don't get your mind absolutely set on being a physicist! Investigate other fields. A certain amount of devotion and work will improve your peformance, but you have to be realistic. There are any number of golfers who aspire to have a 0 handicap, tennis players who work to become champions, chess players who study to be masters. But things don't work out for most of them. If they enjoy the attempt, that's all right. If they drive themselves crazy, it isn't.

The thing is that when you learn many things, you are able to use one template in one area and apply it to another area and this is a very good reason for you to explore different things.

So even if you want to a 'good' physicist or 'good' mathematician, studying what some would call 'completely' unrelated things is a good thing to help you in your 'physics' or 'mathematical' endeavors.

The other thing also is that nature offers so many inspirational ideas and clues about pretty much everything we'd like to know so it would be really stupid if you only paid attention to a very small narrow band of it.

Out of curiosity, do you do any computer programming? Do you have any technical hobbies?

If you post on a physics and math forum and say you are discouraged about your progress in physics and math then naturally the predominant tone of advice is going to be "work harder", "devote yourself". If you want to see the otherside of the coin, you would post on an English literature forum. I haven't looked to see if you've made other posts on the forum. If you've asked questions about homework on the forum then a person could look at them and perhaps say "You've almost got the hang of it" or "Nah, give up, kid." Without some examples, we're just guessing.

You're only a sophomore, so I say don't get your mind absolutely set on being a physicist! Investigate other fields. A certain amount of devotion and work will improve your peformance, but you have to be realistic. There are any number of golfers who aspire to have a 0 handicap, tennis players who work to become champions, chess players who study to be masters. But things don't work out for most of them. If they enjoy the attempt, that's all right. If they drive themselves crazy, it isn't.

I joined this forum no more than three days ago, and I haven't made any posts that would help anybody pinpoint my weaknesses in math. Since I've just joined here though, I'll probably end up using the homework help section and see where that leads to.

I've tried to be as realistic as I can in becoming a physicist, but regardless of my capabilities in math, physics is what I'm passionate about right now, and if I'm able to put a little more effort into math to be able to achieve that goal, then so be it. I can always fall back into a career focused more on writing if it does come to that, or even some other branch of science that doesn't involve such a vast understanding of math, maybe something more revolved around basic calculations, reducing and analyzing data, and error analysis.

Despite my young age, I have actually put a lot of thought into what career I would like to have. Definitely more than the other people at my school. Anyways, I'm kind of rambling, and it's late, so thanks for the help, and I'll try to use the homework help section to narrow down exactly what my issues with math are, and if I will be able to really improve.

Technology has always interested me, but as far as I'm aware, my highschool doesn't offer any programming classes. I've heard that Fortran, C, and C++ are the mainly used languages in computer programming in Physics, are those something that I could teach myself?

The other thing also is that nature offers so many inspirational ideas and clues about pretty much everything we'd like to know so it would be really stupid if you only paid attention to a very small narrow band of it.

If you're saying that it is a bad idea to pick what one wants to be when they grow older at a young age, then I would have to disagree with you. I have my heart and soul set on being a theoretical or experimental physicist. Also, I think it is a tremedous idea to develop an early passion for something and persue it to the fullest IMO.

If you're saying that it is a bad idea to pick what one wants to be when they grow older at a young age, then I would have to disagree with you. I have my heart and soul set on being a theoretical or experimental physicist. Also, I think it is a tremedous idea to develop an early passion for something and persue it to the fullest IMO.

True, but he's also being generous in pointing out that, if for some reason (math) becoming a physicist doesn't work out for me, that I shouldn't be discouraged because there are numerous of other fields that examine nature and how it works, and that narrowing my scope to just one of them would be foolish.

I've heard that Fortran, C, and C++ are the mainly used languages in computer programming in Physics, are those something that I could teach myself?

If you have a computer that you can use intensively, then you can teach yourself programming. (You'll get more advice than you need about what language to learn, once that topic comes up for discussion.)

I, myself, use the Linux operating system and thus get drawn into the practical details of configuring computers. In return for that effort (and sometimes frustration) I can use the free compilers for a vast array of programming languages. Some of these free compilers are also available for Windows.

Computer programming can be very intoxicating and inspiring. If you get the hang of it, you might forget about physics!

I asked you about technical hobbies because I associated an interest in physics with an interest in the practical functioning of the real world. For example, Feynman was interesting in repairing radios when he was a teenager.

I, myself, use the Linux operating system and thus get drawn into the practical details of configuring computers. In return for that effort (and sometimes frustration) I can use the free compilers for a vast array of programming languages. Some of these free compilers are also available for Windows.

Computer programming can be very intoxicating and inspiring. If you get the hang of it, you might forget about physics!

I asked you about technical hobbies because I associated an interest in physics with an interest in the practical functioning of the real world. For example, Feynman was interesting in repairing radios when he was a teenager.

There is also the possibilty of using Matlab. That will be my goal after I start and finish C. I'm mainly going to use it for writing mathematical and physics equations.

I'm asking this because I perhaps physics is not what you think it is. Physics is very math intensive. If you want to philosophize about time travel, wormholes, multiple universes, then physics is not for you.

Perhaps it's wise to get a proper physics textbook and try to read it in order to see if it is something you would like.

Anyway, being weak in math is not a bad thing. You can always improve yourself by practicing. But if you want to improve yourself, then it is important to know where things are going wrong. It makes no sense to practice linear systems of equations if your weakness lies in trigonometry.
Perhaps you can post here some questions that you are having difficulty with?? For example, post some questions that you weren't able to solve on your last test. Perhaps we can advise you better then.

Mathematics are to be studied with afterthought and with peace of mind. Always make sure you're in a silent and comforting surrounding when studying anything really, although especially mathematics.

In a more subjective sense, I've never experienced any benefits of studying in groups while learning a new subject. However, trying to explain concepts you think you know to your peers surely puts your knowledge to test and it is a good way to determine whether or not you need to study the concepts more in depth.

I'm sure that most people are naturally intrigued to concepts like time travel and worm holes and similar ideas, but for me, it's just the idea of being a physicist, as generic as that sounds.

Expanding my knowledge in ways, especially in something that I feel that I maybe wasn't built for (not that I doubt my capacity to improve in the areas that I'm currently lacking in) really appeals to me. The idea of being able to actually understand how the universe works, and have a better overall understanding of the world that we live in, like I said earlier, really appeals to me.

Not to mention, science in general is an interesting way of life. Having a job where I'm pushing myself, and possibly human knowledge, to the edge of its capacity and trying to learn what we previously did not know, has this sense of inspiration encompassing it.

--
I'll make a post after this one showing one of my most recent questions (not on my most recent test, since our last one was several weeks ago, and I actually did relatively well on it aside from a few minor mistakes) dealing with irrational algebraic functions.

[...]for me, it's just the idea of being a physicist, as generic as that sounds.

[preaching]
Ideally, what you should want is to do what Fs do, rather than to be an F. A lot of people, it seems to me, pursue careers or "interest" which they think will make them happy and satisfied, because they've created this romantic fiction in their head about how wonderful it is to be an F. Please save yourself from making that mistake. Do what you're passionate about doing instead.
[/preaching]

[preaching]
Ideally, what you should want is to do what Fs do, rather than to be an F. A lot of people, it seems to me, pursue careers or "interest" which they think will make them happy and satisfied, because they've created this romantic fiction in their head about how wonderful it is to be an F. Please save yourself from making that mistake. Do what you're passionate about doing instead.
[/preaching]

It seems like you ignored the rest of my post, but I've put a lot of thought into this, and understand what a physicist does. What they do interests me.

Thanks for the concern, though. I probably worded that poorly, now that I think about it.

Forgive me if this is the wrong place to be posting this, but as far as I can tell, this is the most appropriate place to post my question that I can find.

My main question is obviously the title of this thread, but I figured that it would be best for me to give you some background information about my own mathematic abilities in order to make it easier for a response:

I'm currently a sophomore in higschool, and am one year ahead in math, take all Honors and AP classes, but in math, I always seem to struggle to get Bs. It's discouraging to see other people in my class, some of them even a year younger than me, who seem to grasp the concepts with ease, while I'm going home and spending hours going through problems just trying to make sure I know everything.

Now, unfortunately, I fear that my intelligence and my ability to do well in school revolves around my memory and my ability to write well. I would easily give up those skills to obtain a more analytical mind so that I could potentially pursue a career in Physics, and not be way in over my head.

So, my main question is this: Are there any definitive ways for somebody to improve at math? I've heard that a lot of it is the ability to get the main ideas of it down, and to then learn how to apply those concepts to more complicated ideas. Would it be best for me to almost re-learn the basics of each course that I've taken so far?

Also, in a related note, is it worth pursuing a career in Physics if it interests me, when I am stronger in other subjects? I try to think of myself as a humble person, but just this year, my English teacher was bombarding me with praise. I got 100% on virtually all of my essays, and in one assignment that I wrote (a prequel to the Scarlet Letter) she told the class (apparently when I was gone that day) that she couldn't have written it better herself. I wrote it in one hour at 2 in the morning..

I'm sort of in a dilemma right now where Physics is my passion, it's what interests me, but my mind appears to work better for other things.

I'm taking AP Physics next year, so as far as I can tell, that will be the best guideline to tell me whether or not I'll be able to just work towards learning and understanding Physics. I'm fully aware that being a phsyicist obviously isn't something for everyone (there's some statistic where the average IQ of a physicist is 148, or something around that), but I want to know if math is something that a person could substantially improve on through hard work, and if so, what the best ways to achieve that goal are.

Thanks for reading.

When I was your age, I was terrible at math. This was solely a combination of bad instruction and a lack of effort on my part (The two were probably related). I'm now in a PhD program in physics where probably my greatest attribute is my intuition and knowledge of mathematics. Yes, practice is what makes a mathematician and physicist. To be very, very good at mathematics requires you to think very long and very hard, to practice many many times, and in some sense you need to have an aptitude for it. But I will say that at your age, there's not going to be an issue of aptitude. You're still a bit young, and your brain is developing. This is true of your peers, as well. In 5 years time, your friends who're doing great in AP math could be pre-meds who're utterly clueless and forgot everything about calculus and algebra (This happens very often).

I suppose my point is the following: If you think you want to be a physicist or mathematician, now is not the time to be concerned about your aptitude. If you think you like it, give it your best effort. If you end up not liking it/not finding the desire to train yourself in mathematical abilities, then perhaps it's for the best and another career path is meant for you. Until then, however, you should read and understand mathematics as best you can. And next year, you should see how well you like physics. Physics and mathematics are challenging disciplines, it is hard work to become very good at them at the undergraduate, graduate, and especially professional level.

In answer to your question --work hard on mathematics. Especially, think about how to prove different formulas using algebra and calculus, and also how practice general techniques and expanding techniques for solving equations.

It seems like you ignored the rest of my post, but I've put a lot of thought into this, and understand what a physicist does. What they do interests me.

Thanks for the concern, though. I probably worded that poorly, now that I think about it.

Well, not really. It was the rest of the post that made me think that you're striving towards some romantic fiction. If you're going work in academia what you will be doing is probably something like working for 48 hours a day while not understanding things and failing to make important contributions. Every day. For pretty much the rest of your life. If you take a field seriously, you will be challenged, and you will probably feel that you maybe wasn't built for it at many times. I personally don't think that that is a bad life, but it doesn't really match what you wrote. Furthermore, the only thing in your post that is in any way specific to physics is what I quoted, and that's why I quoted it.

I'm not quit sure why I wrote that post though. It probably has something to do with the time being close to 02:30 at night over here...

Well, not really. It was the rest of the post that made me think that you're striving towards some romantic fiction. If you're going work in academia what you will be doing is probably something like working for 48 hours a day while not understanding things and failing to make important contributions. Every day. For pretty much the rest of your life. If you take a field seriously, you will be challenged, and you will probably feel that you maybe wasn't built for it at many times. I personally don't think that that is a bad life, but it doesn't really match what you wrote. Furthermore, the only thing in your post that is in any way specific to physics is what I quoted, and that's why I quoted it.

I'm not quit sure why I wrote that post though. It probably has something to do with the time being close to 02:30 at night over here...

No worries, and I definitely see where you're coming from. Not to mention, there's the issue of even finding a stable job after earning your PhD once you graduate...

FieldTheorist, thanks for the response. It's at least nice to see it from somebody else who was in a similar situation as me. I probably am worrying a little bit too much about being behind in math. It doesn't help that I've been reading around in a forum that is the home of various types of PhDs, so I shouldn't be surprised that their knowledge and understanding of math far surpasses my own.

So that I don't double post again, I'm going to include one specific example of me not understanding math, that I think shows the issue that I usually have with it:

First off, this was the first time that I had seen a problem like this, and I thought that I was being smart and started off solving it (incorrectly). Here's the original equation, and I'll show how I tried to solve it. Side note, I'm aware that it is only showing one part of a square root symbol, but know that √2 is the square root of two, regardless of the missing part:

3/(1 + √2 - √3)

3(1 - √2 + √3)/1-2-3 <- In my mind, (1 - √2 + √3) was the conjugate, so I
multiplied both the numerator and denominator by it, thinking that it would cancel out the radicals in the denominator.

3(1 - √2 + √3)/-6 <- That's how far I got before I looked up and saw the correct way (the way my teacher was doing it):

Then for the rest of it, you just multiple the top and bottom by √2 to get rid of the radical in the denominator and solve it... I'm fine with that.

I just don't understand why multiplying the numerator and denominator by [(1 + √2) + √3] works, as opposed to what I originally thought: (1 - √2 + √3)

Do conjugates only work for binomials, and if so, then why is the term outside of the parentheses the one that changes? It's almost like the mathematical logic of my mind is different from the way it actually works sometimes, especially when my teacher doesn't explain why something works, and why something else doesn't.

Sorry if that was sloppy, or hard to follow, that's the first time that I've ever typed out math....